High-Dimensional Variable Selection With Reciprocal L₁-Regularization

REFERENCES

• Akaike, H. (1974), “A New Look at Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723.
   Web of Science ®Google Scholar
• Breheny, P., and Huang, J. (2011), “Coordinate Descent Algorithms for Nonconvex Penalized Regression, With Applications to Biological Feature Selection,” The Annals of Applied Statistics, 5, 232–243.
   PubMed Web of Science ®Google Scholar
• Candes, E., and Tao, T. (2007), “The Dantzig Selector: Statistical Estimation When p is Much Large Than n,” Annals of Statistics, 35, 2313–2351.
   Web of Science ®Google Scholar
• Chen, J., and Chen, Z. (2008), “Extended Bayesian Information Criteria for Model Selection With Large Model Spaces,” Biometrika, 95, 759–771.
   Web of Science ®Google Scholar
• Chen, J., and Chen, Z. (2012), “Extended BIC for Small-n-Large-p Sparse GLM,” Statistica Sinica, 22, 555–574.
   Web of Science ®Google Scholar
• Davidson, K., and Szarek, S. (2001), “Local Operator Theory, Random Matrices and Banach Spaces,” in Handbook on the Geometry of Banach Spaces, eds. W. Johnson and J. Lindenstrauss, Amsterdam: North-Holland, pp. 317–366.
   Google Scholar
• Efron, B. (1981), “Nonparametric Standard Errors and Confidence Intervals,” Canadian Journal of Statistics, 9, 139–158.
   Google Scholar
• Chen, J., and Chen, Z. (1982), The Jackknife, the Bootstrap and Other Resampling Plans (Vol. 38), Philadelphia, PA: SIAM.
   Google Scholar
• Efron, B., Hastie, T., Johnston, I., and Tibshirani, R. (2004), “Least Angle Regression,” Annals of Statistics, 32, 407–499.
   Web of Science ®Google Scholar
• Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
   Web of Science ®Google Scholar
• Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultrahigh Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911.
   PubMed Web of Science ®Google Scholar
• Fan, J., and Song, R. (2010), “Sure Independence Screening in Generalized Linear Model With NP-Dimensionality,” Annals of Statistics, 38, 3567–3604.
   Web of Science ®Google Scholar
• Foygel, R., and Drton, M. (2010), “Extended Bayesian Information Criteria for Gaussian Graphical Models,” in NIPS, pp. 604–612.
   Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Haario, H., and Saksman, E. (1991), “Simulated Annealing Process in General State Space,” Advances in Applied Probability, 23, 866–893.
   Web of Science ®Google Scholar
• Johnson, V. (2013), “On Numerical Aspects of Bayesian Model Selection in High and Ultrahigh-dimensional Settings,” Bayesian Analysis, 8, 741–758.
   PubMed Web of Science ®Google Scholar
• Johnson, V., and Rossel, D. (2012), “Bayesian Model Selection in High-Dimensional Settings,” Journal of the American Statistical Association, 107, 649–660.
   Web of Science ®Google Scholar
• Kirkpatrick, S. (1984), “Optimization by Simulated Annealing: Quantitative Studies,” Journal of Statistical Physics, 34, 975–986.
   Web of Science ®Google Scholar
• Lan, H., Chen, M., Flowers, J., Yandell, B., Stapleton, D., Mata, C., Mui, E., Flowers, M., Schueler, K., Manly, K., Williams, R., Kendziorski, K., and Attie, A.D. (2006), “Combined Expression Trait Correlations and Expression Quantitative Trait Locus Mapping,” PLoS Genetics, 2, e6.
   PubMed Web of Science ®Google Scholar
• Liang, F. (2002), “Some Connections Between Bayesian and Non-Bayesian Methods for Regression Model Selections,” Statistics and Probability Letters, 57, 53–63.
   Web of Science ®Google Scholar
• Liang, F., Cheng, Y., and Lin, G. (2014), “Simulated Stochastic Approximation Annealing for Global Optimization With a Square-Root Cooling Schedule,” Journal of the American Statistical Association, 109, 847–863.
   Web of Science ®Google Scholar
• Liang, F., Liu, C., and Carroll, R. (2007), “Stochastic Approximation in Monte Carlo Computation,” Journal of the American Statistical Association, 102, 305–320.
   Web of Science ®Google Scholar
• Liang, F., Song, Q., and Yu, K. (2013), “Bayesian Subset Modeling for High Dimensional Generalized Linear Models,” Journal of the American Statistical Association, 108, 589–606.
   Web of Science ®Google Scholar
• Reid, S., Tibshirani, R., and Friedman, J. (2014), “A Study of Error Variance Estimation in Lasso Regression,” arXiv:1311.5274.
   Google Scholar
• Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.
   Web of Science ®Google Scholar
• Steck, H., and Jaakkola, T. (2003), “Bias-Corrected Bootstrap and Model Uncertainty,” in Advances in Neural Information Processing Systems, eds. S. Thrun, L. Salu, and B. Schölkopf, pp. 521–528, Cambridge, MA: MIT Press.
   Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the LASSO,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” Annals of Statistics, 38, 894–942.
   Web of Science ®Google Scholar
• Zhang, C.-H., and Huang, J. (2008), “The Sparsity and Bias of the LASSO Selection in High-Dimensional Regression,” Annals of Statistics, 36, 1567–1594.
   Web of Science ®Google Scholar
• Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” Journal of Machine Learning Research, 7, 2541–2563.
   Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.
   Web of Science ®Google Scholar
• Zou, H., and Li, R. (2008), “One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models,” Annals of Statistics, 36, 1509–1533.
   PubMed Web of Science ®Google Scholar